an active front steeringcontrol based on composite...
TRANSCRIPT
AN ACTIVE FRONT STEERING CONTROL BASED ON COMPOSITE
NONLINEAR FEEDBACK FOR VEHICLE YAW STABILITY SYSTEM
MOHD HANIF BIN CHE HASAN
UNIVERSITI TEKNOLOGI MALAYSIA
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To my employer, Universiti Teknikal Malaysia Melaka for supporting my study
To my beloved family for their encouragement and love
AN ACTIVE FRONT STEERING CONTROL BASED ON COMPOSITE
NONLINEAR FEEDBACK FOR VEHICLE YAW STABILITY SYSTEM
MOHD HANIF BIN CHE HASAN
A project report submitted in partial fulfilment of the
requirements for the award of the degree of
Master ofEngineering (Electrical-Mechatronics and Automatic Control)
Faculty of Electrical Engineering
Universiti Teknologi Malaysia
JANUARY 2013
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ACKNOWLEDGEMENT
First of all, thanks to Allah, god and creator of this universe for His blessing
in accomplishment of this research project. I would like to express my gratitude to
my supervisor, Associate Professor Dr Yahaya bin Md. Sam for his guidance and
support. Also special thanks to Universiti Teknikal Malaysia Melaka as my employer
for funding my study.
Besides, not forgettable to our research group members that consists of Mr
Khairi, Ms Norhazimi and Mr Fahezal who are help me directly during the
commencement of the research. Nevertheless, I would like to thanks to my entire
fellow postgraduate student and my family for their support mentally and physically.
Without them, it is impossible for me to go through this process smoothly and
successfully within given period.
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ABSTRACT
Vehicle stability control (VSC) is one of important topics in vehicle dynamics
and active automotive control. This research is focusing on vehicle stability control
by active steering system that utilizes steering control method to improve stability of
the vehicle. This stability control system is solely based on kinematic and dynamics
motion of vehicle. The development of mathematical model of vehicle dynamic that
includes body and tyre dynamics is one of the most important steps to make sure the
result obtain is close as possible to actual system. In the other hand, an analysis of
transient state is very crucial in control system performance where one of the
objectives is to track reference signal as fast as possible with minimum overshoot,
fast settling time, and without exceed nature of actuator saturation limit. Hence, in
order to achieve this target, a robust and high performance of control algorithm is
essential for vehicle stability control. In this research project report, a Composite
Nonlinear Feedback (CNF) strategy is used to control yaw rate of vehicle through
active steering. Extensive computer simulation is performed with considering a
various profile of cornering manoeuvres with external disturbance to evaluate its
performance in different scenarios. The performance of the proposed controller is
compared to conventional Proportional Integration and Derivative (PID) for
effectiveness analysis.
vi
ABSTRAK
Kawalan kestabilan kenderaan adalah salah satu topik penting dalam dinamik
kenderaan dan kawalan aktif kerangka. Kajian yang dijalankan ini akan difokuskan
pada kawalan kestabilan melalui sistem stering aktif yang menggunakan kaedah
kawalan stering bagi memperbaiki kestabilan sesebuah kenderaan. Sistem kawalan
kestabilan ini berasakan sepenuhnya kepada gerakan kinamatik dan dinamik
sesebuah kenderaan. Pembinaan model matematik bagi dinamik kenderaan yang
melibatkan dinamik keranka dan tayar adalah salah satu langkah penting untuk
memastikan keputusan yang diperolehi adalah sehampir yang mungkin dengan
sistem yang sebenar. Selain itu, analisis keadaan fana adalah sangat penting dalam
prestasi sistem kawalan dimana salah satu objektif adalah menjejaki isyarat rujukan
secepat mungkin dengan penghasilan telajak yang minimum, masa reda yang cepat,
dan tanpa melepasi tahap tepu yang normal bagi sesebuah penggerak. Oleh itu,
dalam mencapai sasaran ini algoritma pengawal yang mantap dan berprestasi tinggi
adalah menjadi satu kemestian dalam kawalan kestabilan kenderaan. Dalam laporan
kajian ini, strategi Komposit Suapbalik Tak linear (CNF) digunakan untuk mengawal
kadar rewang kenderaan melalui kaedah stering aktif. Simulasi komputer yang
ekstensif digunakan dengan mengambil kira pelbagai gerakan dan profil selekoh dan
juga gangguan luaran untuk menilai tahap kecekapan kawalan yang dibina dalam
situasi-situasi berbeza. Kebolehan pengawal yang disyorkan akan dibandingkan
dengan pengawal Perkadaran, Pengamiran dan Pembezaan (PID) yang konvensional
untuk menganalisis tahap kecekapan.
vii
TABLE OF CONTENTS
CHAPTER TITLE PAGE
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENTS iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENTS vii
LIST OF TABLES ix
LIST OF FIGURES x
LIST OF ABBREVIATIONS xii
LIST OF SYMBOLS xiv
1 INTRODUCTION 1
1.1 Vehicle Stability 1
1.2 Project Overview 3
1.3 Objective of Study 4
1.4 Scope of Project 5
1.5 Research Methodology 5
1.6 Literature Review 8
2 SYSTEM MODEL 15
2.1 Introduction 15
2.2 Modelling of Two Track Yaw Plane Vehicle 16
2.3 Modelling of Tyre Dynamic 21
2.4 Linearization for Constant Velocity and Small Angle 25
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2.5 Reference Model 28
2.6 Type of Performance Test 30
2.7 Conclusion 32
3 CONTROLLER DESIGN 33
3.1 Introduction 33
3.2 Control Scheme and Objective 34
3.3 Composite Nonlinear Feedback 35
3.3.1 Basic CNF 36
3.3.2 Enhance CNF 39
3.4 Stability Analysis 44
3.4.1 Basic CNF Stability 45
3.4.2 Enhance CNF Stability 46
3.5 Conclusion 48
4 SIMULATION 49
4.1 Introduction 49
4.2 CNF Based Active Front Steering 49
4.3 Result and Discussion 52
4.3.1 J-Turn Manoeuvre with Disturbance 53
4.3.2 Single Sine Manoeuvres with Disturbance 57
4.4 Conclusion 66
5 CONCLUSION AND RECOMENDATION 68
5.1 Conclusion 68
5.2 Recommendation 69
REFERENCES 70
ix
LIST OF TABLES
TABLE NO. TITLE PAGE
2.1 Numerical data used for the vehicle (He 2005) 20
2.2 Numerical data used for the Pacejka tyre model 25
4.1 Numerical parameters for Basic and Enhance CNF
Controllers
51
4.2 Performance of controllers during step input 56
x
LIST OF FIGURES
FIGURE NO. TITLE PAGE
1.1 Understeering and oversteering situations 3
1.2 Research methodology flow chart 6
2.1 Nonlinear two track yaw plane vehicle model 17
2.2 Wheel rotation motion on top and side view 19
2.3 Lateral Tyre Force versus tyre slip angle 23
2.4 Lateral Tyre Force in combined slip condition 24
2.5 Longitudinal Tyre Force in combined slip condition 24
2.6 Yaw rate response for three different approaches 29
2.7 J-Turn manoeuvre 31
2.8 Various amplitude of single sine steering manoeuvres 31
2.9 Side wind external disturbance 32
3.1 AFC steering actuation 34
3.2 AFC block diagram configuration 35
4.1 Actual and estimate value of disturbance 52
4.2 J-Turn input steer with disturbance 54
4.3 Side slip during J-Turn input with disturbance 54
4.4 Yaw rate during J-Turn input with disturbance 55
4.5 Tracking error of yaw rate during J-Turn input with
disturbance 55
4.6 Active steer (controller output) during J-Turn input with
disturbance 56
4.7 Input for 2° single sine amplitude with disturbance 58
4.8 Side slip during 2° single sine amplitude with disturbance 58
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4.9 Yaw rate during 2° single sine amplitude with
disturbance 59
4.10 Tracking error of yaw rate during 2° single sine
amplitude with disturbance 59
4.11 Active steer (controller output) during 2° single sine
amplitude with disturbance 60
4.12 Input for 3.1° single sine amplitude with disturbance 60
4.13 Side slip during 3.1° single sine amplitude with
disturbance 61
4.14 Yaw rate during 3.1° single sine amplitude with
disturbance 61
4.15 Tracking error of yaw rate during 3.1° single sine
amplitude with disturbance 62
4.16 Active steer (controller output) during 3.1° single sine
amplitude with disturbance 62
4.17 Input for 7.1° single sine amplitude with disturbance 63
4.18 Side slip during 7.1° single sine amplitude with
disturbance 64
4.19 Yaw rate during 7.1° single sine amplitude with
disturbance 64
4.20 Tracking error of yaw rate during 7.1° single sine
amplitude with disturbance 65
4.21 Active steer (controller output) during 7.1° single sine
amplitude with disturbance 65
4.22 Yaw rate during 7.1° single sine amplitude with
disturbance (Without desired yaw rate saturation) 66
xii
LIST OF SYMBOLS
� - Wheel steering angle
��� - Braking torque at ith wheel
� - Vehicle velocity at centre of gravity
� - Vehicle side slip angle
�� - Vehicle yaw rate
�� - Desired vehicle yaw rate
� - Sideslip angle at ith wheel
�� - Tyre longitudinal slip ratio at ith wheel
�� - Tyre ground contact point velocity at ith wheel
�� - Tyre rotational speed at ith wheel
�� - Longitudinal tyre force at ith wheel
�� - Lateral tyre force at ith Wheel
�� - Tyre normal load at ith Wheel
��� - Nominal tyre cornering stiffness at front wheel
��� - Nominal tyre cornering stiffness at front wheel
�� - Distance from the vehicle center of gravity to the front axle
�� - Distance from the vehicle center of gravity to the rear axle
� - Wheel base of vehicle
T - Track of vehicle
h - Vertical distance from CG of sprung mass to roll axis
�� - Moment of inertia of car body
�� - Wheel moment of inertia
R - Tyre radius
m - Total mass of the vehicle
µ - Road adhesion coefficient of road
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�� - Steering wheel ratio
� - Gravity = 9.81 m/s-2
� - Nonlinear locally Lipschitz function
�� - Linear state feedback of CNF
�� - Nonlinear state feedback of CNF
� - 1st nonlinear parameter gain of CNF
� - 2nd nonlinear parameter gain of CNF
! - State equilibrium point
" - Reference signal of control system
#$ - Damping ratio of closed loop system
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LIST OF ABBREAVIATIONS
VSC - Vehicle Stability Control
ASC - Active Steering Control
AFS - Active Front Steering
ESP - Electronic Stability Program
DYC - Direct Yaw Moment Control
FWS - Front Wheels Steering
4WS - Four Wheels Steering
CNF - Composite Nonlinear Feedback
PID - Proportional Integration Derivative
SMC - Sliding Mode Control
ISM - Integral Sliding Mode
LQR - Linear Quadratic Regulator
MPC - Model Predictive Control
LMI - Linear Matrix Inequalities
QFT - Quantitative Feedback Theory
DOF - Degree of Freedom
CG - Center of Gravity
SISO - Single Input Single Output
MIMO - Multi Input Multi Output
IAE - Integral of Absolute Error
ITAE - Integral of Time multiplied Absolute Error
1
CHAPTER 1
INTRODUCTION
1.1 Vehicle Stability
Safety factor is very important issue in vehicle design and handling. Vehicle
safety system can be divided into two parts, which are passive and active safety
system. Passive safety technologies can be seen such as belts, safety glass, and air
bags. The systems are designed to prevent or reduce the damage to the pedestrians,
passengers, and the vehicles involved after the accident has occurred. Meanwhile, in
driver assistance and active safety system have received much attention from
researcher because it can prevent vehicle from accident. Their development is
continuously conducted to meet current demand that always keep increasing on the
safety of vehicles. For example, vehicle stability control (VSC), collision avoidance
(CW/CA), smart cruise control (SCC), lane keeping support, lane change assistance
and collision warning, and automated parking assistance have been extensively
studied with many developments that have been explored since the 1990s (Yu et al.
2008).
The improvement and enhancement of vehicle dynamic control using active
control such active steering control, intelligent braking system, traction control,
active suspension system and combination of these methods are actively conducted
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so that a ground vehicle will have a better stability and handling quality which can
provide safety and comfort driving for the driver. Vehicle stability control (VSC) is
one of the important topics in vehicle dynamics and active chassis control and
purposely to maintain the vehicle keep on the road or desired track/path where lateral
force that exists in vehicle dynamic motion has great influence to the vehicle
stability.
Yaw stability control system that purely based on kinematic and dynamics
motion of vehicle is one of lateral control system that has been developed by
researchers. The main objectives of vehicle yaw stability control are to control the
yaw rate, vehicle sideslip or combination of them. Two major approaches of yaw
stability control are using active steering control (ASC) and direct yaw moment
control (DYC) that based on braking system such as active differential or active
braking. A dynamic motion of vehicle is very nonlinear due to its robustness of
uncertainties characteristics and disturbance that have great influences to vehicle
stability. Hence, in order to cater this problem, a robust control algorithm is essential
for vehicle stability control. These systems are believed to reduce the risk of
accidents, improve safety, and enhance comfort and performance for drivers. The
introduction of these new advanced driver assistance and active safety systems open
new possibilities in accident prevention.
Active steering is an effective tool and most popular to control vehicle
handling in where active front steering type has attracted more and more attention.
Originally, this technology developed by German BMW Company and ZF
Lenksysteme GmbH Company in 2003 as optional equipment for BMW vehicle from
E60 5 Series and E63 6 Series models. This type of active front steering is use a
power electric variable gear ratio power steering technology. The gear ratio is been
controlled such that varies the degree that the wheels turn in response to the steering
wheel. For the next generation's vehicle, the steer by wire system (SBW) is the one
of the advanced technologies that will replace current electro mechanical system.
The advantage of this system is it can prevent mechanical linkages of column shaft
between steering wheel system and front wheel system.
3
1.2 Project Overview
In vehicle stability control, there are two common situations of vehicle
dynamic during unstable condition that called understeering and oversteering as
shown in Figure 1.1. Others possible situation occurred when vehicle disturbed by
side wind and split road coefficient. All these conditions can be controlled by using
Active Steering, Differential Braking, Traction Control, Active Suspension, or
combination of these strategies.
Figure 1.1 Understeering and oversteering situations
A skid normally occurs when the speed of the car is too fast for the normal
road conditions. A skid hardly ever occurred at a slow speed. Severe braking can also
cause a skidding. Many dangerous situations occurred on the roads because a car
driver does not react fast enough at the beginning of skidding or rollover. Even on a
normal road, sudden movement of the steering could make a car skid and will cause
a critical driving situation. For example, when child crossing the road unexpectedly,
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this will force the driver to an evasive action. The inexperienced driver who caught
in this kind of situation will easily overreact and destabilizes the car.
The aim of this study is to use CNF based active front steering control for
vehicle yaw stability control of typical passenger cars for general some cornering
manoeuvres with external disturbance. A vehicle control system using a 2 DOF
controller that based on Composite Non-Linear Feedback (CNF) algorithm, will be
proposed to enhance vehicle stability and improve system response especially during
transient state.
1.3 Objective of Study
This research embarks on the following objectives:
I. To establish the dynamics modelling of vehicle.
II. To propose an Active Front Steering (AFS) based on Composite Nonlinear
feedback (CNF) for Vehicle Stability Control (VSC).
III. To enhance performance of Vehicle Yaw Stability by using the proposed
controller.
To achieve these objectives, various parameters involved such as vehicle
construction parameters, tyre coefficient, and velocity will be considered. The
vehicle modelling that involved body and tyre dynamic will be explored. Two main
vehicle outputs, which play main important factor of vehicle stability, vehicle side
slip and yaw rate will be observed and demonstrated by using the computer
simulations. Performance of the proposed controller will be compared to
conventional PID technique. Theoretical verification of the proposed controller on its
stability and reachability will be accomplished by using a Lyapunov’s second
method theory. The performance of the AFS system will be then observed by using
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extensive computer simulation that will be performed using MATLAB software and
SIMULINK Toolbox subjected to various types of test manoeuvres and disturbance.
1.4 Scope of Project
The research work carry out in this project are concentrated to the following aspects:
I. Mathematical modelling of vehicle body and tyre dynamic vehicle using
Matlab Simulink.
II. Implementation of Composite Nonlinear Feedback (CNF) control scheme for
Active Front Steering (AFS) control in vehicle yaw stability system.
III. Simulation, validation and analysis of the Composite Nonlinear Feedback
(CNF) performance based Active Front Steering (AFS) method.
IV. Evaluation of Composite Nonlinear Feedback (CNF) based Active Front
Steering (AFS) control performance with Proportional Integral Derivative
(PID) control strategy.
Research in vehicle stability is very wide to be explore, so some parameter
need to be ignored without scarifies important factors involved in this CNF based
active front steering research.
1.5 Research Methodology
The methodology of this research can be described by flow chart as shown in Figure
1.2.
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Figure 1.2 Research methodology flow chart
Start point of this research is a literature review where existing founding of
vehicle stability conduct by researcher need to be carry out. On this stage,
fundamental knowledge is very important. The basic knowledge for physic law
applied in vehicle body and tyre dynamic need to be refreshing. Basic control
knowledge such as state space, differential equation and stability law, include control
strategy have to straighten as well. Thus, besides reading research papers, some
fundamental books also need to read out. Besides of doing literature review,
exercises and tutorials need to be done for mastering the simulations tools and some
preliminary simulations need to be carried out as well.
7
The next step for this research is development of plant model. On this stage,
car model based on two-track yaw plane have been carried out. Vehicle modelling
contains body and tyre dynamics. A car body dynamic with 7 Degree of Freedom
(DOF) will be constructed to model a vehicle as closed as actual one. Tyre dynamic
model also is considered and in this research, Magic Formula is used in tyre
modelling due to it is widely used by researchers. This research will be stressed on a
dynamic mathematical modelling of vehicle and CNF control algorithm. The
performance of proposed controller then will be evaluated by different types and
level of car manoeuvres on nominal road adhesion coefficient, speed and disturbance
as well. The task is to ensure stability, prevent skidding of vehicle, and remain the
car at the desired path. This will be considered of the dynamics relationship of a car
and take into account the yaw movement and lateral motion that make the car
unstable.
The Active Front Steering system control strategy is required to minimize the
yaw rate and side slip angle errors of vehicle during cornering manoeuvre. Various
parameters will be observed such as relationship between slip angles and lateral
forces on tire and uncertainties on the friction of the road surface and vehicle speed.
Relationship on vehicle inputs, which is front wheel steering angle applied effect on
vehicle side slip and yaw rate without controller have been evaluate by Matlab
simulation software as preliminary result. Even though active steering control can
overcome some of the vehicle handling problem, it only capable to drive the vehicle
at moderate cornering level only. To overcome this limitation, controller with
integration of active breaking is more effective method especially during high
vehicle speed where tyre vehicle dynamic start to react in nonlinear regime. This
automatic feedback system can assist the driver to overcome such dangerous
situations. Robustness of the control system with respect to the various cornering
manoeuvres and disturbance are very important.
After establish plant model and consider of control strategy, control solution
has been considered. Basic controlling algorithm will be evaluated first. In this stage,
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famous conventional Proportional Integration and Derivative (PID) method is used.
Then, new control strategy for active front steering car system will be proposed
based on the Composite Nonlinear Feedback Control (CNF) approach. A CNF
technique is proposed to improve the performance of the vehicle stability and road
handling characteristic of the car especially at transient stage. To ensure the
robustness of the proposed controller, various cornering manoeuvres together with
disturbance will be applied to the system.
Finally, the proposed controller will be evaluated with extensive simulation
work to determine the performance. Then, the performance of the system using CNF
will be compared with PID technique, which is performed in previous work. The
results will be then verified and analysed in time domain as typical linear analysis.
1.6 Literature Review
Vehicle stability implementation by active steering control can be seen in
many research papers, mostly by Active Front Steering (AFS) (Q. Li et al. 2009;
Ohara & Murakami 2008; Ma et al. 2010; Zhang et al. 2008; Mammar & Koenig
2002; Nam et al. 2009; Zheng & Anwar 2009; Kawaguchi et al. 2007; Guo & Feng
2011; Falcone, Borrelli, et al. 2008; Y. C. Chen et al. 2010; Marino et al. 2011;
Kunsoo Huh 1999; Nor Maniha 2006; Fujimoto & Yamauchi 2010; Wanzhong et al.
2011; Namuduri et al. 2009; Wen et al. 2009; Q. Li et al. 2010; Solmaz, Corless & R
Shorten 2007; Yamauchi & Fujimoto 2008). This is an effective way to ensuring
stable cornering at moderate levels by driver commanded steering. Based on active
steering actuator, there are two type of approach available today which are
Mechatronics-angle-superposition and a new steer-by-wire (SBW) technology. For
old approach, such in Tongue (2005) show a BMWs active steering mechanism who
is a pioneer of this front steering system technology. Implementation of fully steered
wheel control (Both front and rear wheels), also known as Four Wheel Steering
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(4WS) is another type of active steering system and can be found in some papers (B.
Li & Yu 2009; F. Du et al. 2010; Nor Maniha 2006; Ghani & Sam 2007; Wen et al.
2009) and even though this method seems more complicated but it is more efficient
way to control vehicle stability. This can be seen during high level of speed
cornering, the steady yaw rate of vehicle for 4WS is less than AFS that means at
same cornering, driver workload can be reduced drastically.
Direct Yaw Moment Control (DYC) method also widely used by researchers
(Mirzaei 2010; B. L. Boada et al. 2005; Canale et al. 2008) until today. It is an
effective solution for high tyre slip angles, where tyre region is not linear anymore.
To extend performance of a stability system in wider range, ASC and DYC
Integration (He 2005; Ding & Taheri 2010; Falcone, Eric Tseng, et al. 2008; Tjønnås
& Johansen 2010; Baslamisli et al. 2011) was made. Besides, others methods are
such as controlling vehicle stability by Integration of ASC and Active Suspension
(Lai & Deng 2009) and ASC and DYC with Active stabilizer also available (D. Li et
al. 2008). These methods proposed by researchers to improve vehicle limit
performance and mainly to enhance ride comfort.
From all these papers that have been read, maximum degree of freedom
(DOF) for nonlinear vehicle model used is 27 which use CarSim vehicle dynamic
modelling software from Mechanical Dynamics Corporation (MSC) (B. Li & Yu
2009; Marino et al. 2011; Nam et al. 2009; Solmaz, Corless & R Shorten 2007;
Solmaz, Corless & Robert Shorten 2007). Reduce order version of 14 DOF vehicle
model also been used (Canale & Fagiano 2010; Kunsoo Huh 1999). The 8 DOF
vehicle model as in F. Du et al. (2010) and He (2005) is a simplify version which
present roll, yaw, longitudinal, lateral and rotation motion of four wheels of car. By
assuming stiff suspension of vehicle will simplify again vehicle body dynamic,
producing vehicle model of 7 DOF (Ma et al. 2010; Mammar & Koenig 2002; Nam
et al. 2009). The 7 DOF is so called nonlinear yaw plane two track model is less
complex and low computational burden, thus become favour among researcher. The
use of 2 DOF vehicle model (Q. Li et al. 2009; Ohara & Murakami 2008; Y. C. Chen
et al. 2010; Fujimoto & Yamauchi 2010; Q. Li et al. 2010) is still available and it is a
10
basic modelling to present vehicle motion. Other than that, the ADAMS/CAR
software also is used for simulation result validation (Zhang et al. 2008; Guo & Feng
2011). This software is highly dependable and it used to simulate the real vehicle
before the prototype is built (Westborm and Frejinger, 2006).
In the research of active steering, most of researcher did not mention about
type of tyre dynamic equation used in their controlled plant. This is because of in this
control system, tyres still in linear regime so it is not relevant to discuss about tyre
dynamic where only become important when active braking controller is used.
However, when they use CarSim software to present vehicle plant model
automatically we know that the Magic formula is used. However, without consider
tyre dynamic that may tend to enter nonlinear region we cannot see limitation of
active steering realistically. There is several method to represent tyre model and most
famous one is Pacejka tyre model so called Magic Formula (Ma et al. 2010; Mammar
& Koenig 2002; Kawaguchi et al. 2007; Kunsoo Huh 1999). Other than that, is such
as Dugoff tyre model which use in paperwork of F. Du et al. (2010). Linearize
version of Magic formula also can be used when assuming tyre lateral slip angle is
almost zero (Canale & Fagiano 2010). Even though above mention tyre modelling is
use to formulate a tyre behaviour accurately, but by assuming tyre in linear region is
still relevant to present overall plant behaviour in low level cornering manoeuvres as
in some papers (Ghani & Sam 2007; Fujimoto & Yamauchi 2010).
Various control strategies have been proposed by researchers to improve
vehicle stability by active steering method. As highly demand on electric vehicle
nowadays, research area for typical vehicle now expending into electric vehicle as
well (Nam et al. 2009; Fujimoto & Yamauchi 2010; Yamauchi & Fujimoto 2008;
Wanzhong et al. 2011) and thus open a new field and more opportunities to be
explore.
Four wheel active steering has been investigate base on analysis of deficiency
of conventional 4WS method (B. Li & Yu 2009). A model following control
11
structure based on 2 DOF single track model is designed to follow desired yaw rate
and side slip angle of vehicle. Optimal control theory was used in this research and
reported that this method has better handling performance compare with
conventional one if disturbance is not considered. To cater uncertain parameter that
very complex in vehicle system with external disturbance and perturbation, Sliding
Mode Controller is used by F. Du et al. (2010), for 4WS vehicle model. This robust
controller can overcome greatly influence of uncertain factor on the manoeuvrability
of 4WS car and effectively prevent the loss of vehicle stability. Besides, it also can
ensure the car steering quality by prevent steering from making significant change.
Ohara & Murakami (2008), proposed a Proportional Derivative (PD)
controller for active front steering vehicle. Strength of this research was they use side
slip observer in controlling the yaw rate of vehicle. Side slip angle value, which is
very important for stabilizing a vehicle in real world, cannot obtain directly from
typical sensor. The novel linear observer that has minimum estimation error then was
compared with conventional linear observer.
Controlling of vehicle yaw stability by Fuzzy logic based AFS also can be
seen (Ma et al. 2010). In this method, the yaw rate error and its derivative are applied
to the controller inputs. The performance of designed controller then has been
implementing on 8 DOF nonlinear vehicle model and verified trough simulation and
it is proved that this method capable to control yaw stability of car effectively.
Development of an AFS by Quantitative Feedback Theory (QFT) presented
by Zhang et al. (2008). This type of controller have a robust performance that
required to ensure steering response not influence by uncertain quantities such
vehicle mass, velocity, and road conditions. A multi DOF nonlinear vehicle model
was co simulated by Matlab Simulink and ADAM/CAR to evaluate the performance
of a new controller. Under various manoeuvres and road conditions, the control
system had robust performance to improve the dynamic response so that vehicle
always maintain in it desired path.
12
Mammar & Koenig (2002) proposed Linear Fractional Transformation (LTF)
based feedfoward and feedback H$ control to improve vehicle handling after
investigate stability aspects of vehicle lateral motion. The control action is applied as
a summation of user input and corrective angle produced by controller. The synthesis
method simply allows time domain direct specification objectives such in reference
model matching. By obtain both feedback from both yaw rate and front steering
angle, we can achieves the decoupling of lateral and yaw motion and yaw damping
of vehicle simultaneously (Zheng & Anwar 2009). Trade-off between robust
decoupling and yaw rate damping through adjustment of feedback gain respected to
vehicle velocity can be used for gain schedule steering controller to provide the
desired yaw rate damping while maintain the yaw lateral motion decoupled.
Other than that, there are many others control method proposed in active front
steering such as Adaptive Nonlinear Control (Kawaguchi et al. 2007), Model
Predictive Control (MPC) (Falcone, Borrelli, et al. 2008), Mu Control Theory (Y. C.
Chen et al. 2010), Fuzzy logic (Q. Li et al. 2010) and PID (Namuduri et al. 2009).
As reviewed in previous paragraph, so far there are no research works for
Composite Nonlinear Feedback so called CNF technique applied in vehicle stability.
This is a nonlinear control technique, where consists of a linear feedback law and a
nonlinear feedback law without any switching element. The purpose of linear
feedback is to yield a closed-loop system with a small damping ratio for a quick
response, but not exceeding the actuator limits. The nonlinear feedback then is used
to increase the damping ratio as the system output approaches the target reference, so
that overshoot phenomena can be avoided.
CNF technique has been propose by Z. Lin et al. (1998) as a new method to
achieve accurate tracking in linear system. In that paper, he continues his previous
work with Saberi (1995) and demonstrates the effectiveness of CNF implementation
13
on modern flight control application. Their works extend later by Turner et al. (2000)
for high order multivariable linear system, and successfully demonstrate at
Helicopter pitch control and MIMO missile control and then applied CNF in hard
disk and prove that CNF can beat Time Optimal Control in asymptotic tracking
situation. His group also had expend CNF to more general technique by introduce 3
different cases in control feedback method, i.e. the state feedback, the full order
measurement feedback and reduced order measurement feedback.
Selection of nonlinear gain in CNF is very important to ensure controller can
track smoothly and not sensitive to variation of amplitude of target reference. In that
means Lan & B. M. Chen (2007) review some of nonlinear function and introduce
new function with solution to find suitable value of nonlinear function parameter by
solving minimization problem. They investigate two performance criteria, the
Integral of Absolute Error (IAE) and the Integral of Time multiplied Absolute value
Error (ITAE) where both can be used to tuned nonlinear parameter. This research
work also has been carry out for some researchers (Lan et al. 2010).
Classical CNF control method cannot be implementing directly on singular
system. The study on this matter has be carried out by introduce pre-linear feedback
law to singular system and this guarantee the impulsive freeness (D. Lin et al. 2010).
The CNF solution for system with disturbance proposed by Peng et al. (2005) during
considering friction and nonlinearities in hard disk drive (HDD) servo system. The
enhance CNF control technique has a feature to composite disturbance without
scarifying overall tracking performance. Similar study has been carried out then by
some researcher for a system with unknown constant disturbance (Schmid & Lan
2007; Guoyang & Wenguang 2006).
As part of research in robust CNF to handle disturbance, Cheng & Peng
(2007) introduce a new technique without integrator term as usually used from
previous work. The basic idea of this method is based on combination of disturbance
estimation and compensation into original framework of CNF so the steady state bias
14
of disturbance can be eliminate, with at the same time retain the performance of
initial CNF control.
To track general target reference , CNF can be developed by introducing
reference generator, which able to produce more general reference such as sinusoidal
and others wave profile (Cheng et al. 2007). This method comprises the modified
CNF control law and reference generator to tracking a target reference with fast
settling time without overshoot and proven in XY-table trajectory tracking control.
As been reviewing so far, current CNF technique cannot handle uncertainties
situation, which is normal in most application. Due to this disadvantage, integration
with others controller is necessary. In that means, Mondal & Mahanta (2011)
combine CNF with Discrete Integral Sliding Mode (ISM) to achieve high transient
performance on uncertain systems. As result, new proposed CNF-ISM controller
successfully designed on SISO and MIMO uncertain systems and has superior
transient performance compare with normal ISM.
70
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